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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form. (14x^(3))/(21x^(4)) Answer:

Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.\newline14x321x4 \frac{14 x^{3}}{21 x^{4}} \newlineAnswer:

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Csc, sec, and cot of special anglesright chevron icon

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Q. Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.\newline14x321x4 \frac{14 x^{3}}{21 x^{4}} \newlineAnswer:
  1. Factor Out Common Terms: Factor out the common terms in the numerator and the denominator.\newline(14x3)/(21x4)(14x^{3})/(21x^{4}) can be simplified by dividing both the numerator and the denominator by the greatest common factor of the coefficients, which is 77, and by x3x^{3}, which is the lowest power of xx common to both terms.
  2. Divide Coefficients and Exponents: Divide the coefficients and subtract the exponents of like bases.\newline(1421)⋅(x3/x4)=(23)⋅(x(3−4))=(23)⋅(x−1)(\frac{14}{21}) \cdot (x^{3}/x^{4}) = (\frac{2}{3}) \cdot (x^{(3-4)}) = (\frac{2}{3}) \cdot (x^{-1})
  3. Rewrite Negative Exponent: Rewrite the negative exponent as a reciprocal. x−1x^{-1} is the same as 1x\frac{1}{x}, so the fraction becomes: (23)⋅(1x)=23x(\frac{2}{3}) \cdot (\frac{1}{x}) = \frac{2}{3x}

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